free object
a “generic” algebraic structure over the given set, fulfilling no other equations except those given by the defining axioms
en-US/ˈfɹi ɑbˈd͡ʒɪktv/
en-GB/ˈfɹiː ˈɒbd͡ʒɪkt/
a “generic” algebraic structure over the given set, fulfilling no other equations except those given by the defining axioms